DWYER, V.M., 2004. The influence of microstructure on the probability of early failure in aluminum-based interconnects. The Journal of Applied Physics, 96 (5), pp. 2914-2922

Abstract:

For electromigration in short aluminum interconnects terminated by tungsten vias, the well known
“short-line” effect applies. In a similar manner, for longer lines, early failure is determined by a
critical value Lcrit for the length of polygranular clusters. Any cluster shorter than Lcrit is “immortal”
on the time scale of early failure where the figure of merit is not the standard t50 value (the time to
50% failures), but rather the total probability of early failure, Pcf. Pcf is a complex function of
current density, linewidth, line length, and material properties (the median grain size d50 and grain
size shape factor σd). It is calculated here using a model based around the theory of runs, which has
proved itself to be a useful tool for assessing the probability of extreme events. Our analysis shows
that Pcf is strongly dependent on σd, and a change in σd from 0.27 to 0.5 can cause an order of
magnitude increase in Pcf under typical test conditions. This has implications for the web-based
two-dimensional grain-growth simulator MIT/EmSim, which generates grain patterns with σd
=0.27, while typical as-patterned structures are better represented by a σd in the range 0.4 – 0.6. The
simulator will consequently overestimate interconnect reliability due to this particular
electromigration failure mode.